Journal of Coastal Research
SI
51
87-92
West Palm Beach, Florida
Winter 2010
Grain-Size Trend Analysis for the Determination of Non-Biogenic
Sediment Transport Pathways on the Kwinte Bank (southern North Sea),
in Relation to Sand Dredging
Serafim E. Poulos and Arnaud Ballay
Department of Geography and Climatology
Faculty of Geology and Geoenvironment
National and Kapodistrian University of Athens
Panepistimioupolis, Zografou
15784 Athens, Greece
[email protected]
ABSTRACT
Grain-size trend analysis is applied to the determination of sediment transport pathways over the Kwinte Bank,
southern North Sea; which had been subjected to intensive dredging, within the context of the environmental impact
of dredging activities. On the basis of the results of grain-size trend analysis, focused mainly upon the transportation
of the non-biogenic sedimentary material (<2 mm), it appears that: (i) there is a main sediment pathway over the
western (bank crest) and central (dredged area) part of the bank directed toward the NE; whilst a secondary pathway
is established over its eastern gently-sloping flank, having a SE direction. Further, the present analysis shows that the
area of the central (dredged) depression acts more as a ‘by-passing’ zone rather than as a depo-centre for the nonbiogenic sediments. Comparison undertaken with the results of an earlier investigation, for a non-dredged area at
the northern end of the same bank, reveals that the depression due to dredging modifies significantly the sediment
transport pathways; this may be attributed to a change in the seabed morphology which, in turn, modifies the nearbed hydrodynamics (related to tide and/or storm events).
ADDITIONAL INDEX WORDS: linear sandbank, dredging effects, grain-size trend analysis, southern North Sea.
INTRODUCTION
The establishments of sediment transport direction is one of
the major concerns in the study of sedimentary systems within the marine environment. The analysis of spatial changes in
grain-size parameters (mean, sorting and skewness) is one of
the methods used for the identification of net sediment transport pathways. The initial studies undertaken focused upon
variations of an individual parameter, such as mean grain-size
(e.g. PETTIJOHN, POTTER, and SIEVER, 1972). However, the use of
a single parameter is not always diagnostic for sediment movement because, depending on the type of environment under
consideration, grain-size parameters may increase or decrease
down-drift. A major improvement in grain-size trend analysis
was presented by MCLAREN (1981), who used a combination
of the three main grain-size parameters: mean size, sorting
and skewness. Subsequently, MCLAREN and BOWLES (1985) developed a statistical treatment of the grain-size data, which
provided a 1-D model of net sediment transport, as pathways.
According to the McLaren model, although there are theoretically 8 possible combinations of the above-mentioned statistical parameters, only 2 combinations have a higher possibility
of existing in natural environments, where sediment transport occurs in a downstream direction: (1) finer, better sorted
and more negatively skewed; or (2) coarser, better sorted and
more positively skewed. Subsequently, McLaren’s method has
been used with satisfactory results as in the case of the Severn
Estuary (UK) (MCLAREN et al., 1993), in a fjord of British Columbia (MCLAREN, CRETNEY, and POWYS, 1993); this approach
was eventually standarised, i.e. patented (MCLAREN, 2001).
GAO and COLLINS (1992) re-examined the basic assumptions
of the grain-size trend analysis; they argued that, although
the two cases described previously may be the dominant ones,
the presence of other factors can cause a high level of noise
using the 1-D approach. These investigators have shown further that some trends occur in the transport direction, with
a higher frequency of occurrence than in any other direction.
For comparison, in the McLaren method, it is assumed that
in the transport direction only certain types of trends can occur, whilst others do not occur. Thus, these latter authors developed an analytical procedure for grain-size data, based on
a semi-quantitative filtering technique; this incorporates an
adequate significance test and uses the combined trend of the
two main cases (GAO and COLLINS, 1991, 1992 and 1994a). This
procedure results in the calculation of a 2-D residual pattern
of transport vectors.
The present contribution presents a grain-size trend analysis, following the GAO and COLLINS (1992) procedure, for the
Kwinte Bank in the Belgian part of the North Sea. This method
was adopted, primarily, as it is widely-accepted and has produced good results in tidal environments; and, secondarily, due
to the fact that it has also been applied previously and successfully in the case of the Kwinte Bank (GAO et al., 1994). Within
the context of the environmental impact of dredging activities,
the present trend analysis is focused mainly upon the transportation of the non-biogenic sedimentary material, whose grainsizes have been deduced from their settling velocities. The findings of the present study are discussed further, within the context of the existing knowledge of the hydrodynamics, whilst the
effect of dredging is examined through comparison with earlier
Journal of Coastal Research, Special Issue No. 51, 2010
88
Poulos and Ballay
investigations undertaken on the Kwinte Bank (e.g. BELLEC et
al., this volume; GAREL, this volume; GAO et al., 1994; LANCKNEUS, 1989; and VAN DEN EYNDE et al., this volume).
THE STUDY AREA
The present investigation concerns one of the sandbanks
located off the Belgian coast, i.e. the Kwinte Bank (Figure
1.); this is one of a series of NE-SW trending linear sandbanks. These banks are some 10-20 m in height, overlain by
water depths of less than 10 m, over their shallowest parts.
Superimposed upon these banks are N-NW / S-SE trending
dunes (widths of several tens of metres and heights of up to 7
m) and megaripples, with spatially-variable asymmetric patterns. Such linear sandbanks are formed in an environment
associated with strong currents. High-resolution reflection
seismic surveys have revealed that the banks consist mainly
of Holocene deposits, with the sands being supplied by the
reworking of Tertiary and/or Pleistocene deposits (LIU, MISSIAEN, and HENRIET, 1992). The deposits lie on an erosional
surface of Tertiary strata, whose upper layer is comprised
mostly of gravely material. The formation of these sandbanks
is related strongly to the existing hydrodynamic regime and,
in particular, to the tidal currents and storm waves; the
former reach mean surface speeds of between 0.9 ms-1 and
1.2 ms-1 offshore of the Belgian coast (HOWARTH and PROCTOR,
1992), whilst the latter can reach significant wave heights up
to 5 m, with significant periods of 7 s (HOUTHUYS, TRENTESAUX,
and DE WOLF, 1994). Thus, storm waves restrict the vertical
growth of the Flemish Banks to water depths of less than 5
m (MLLWS).
The present investigation is focused upon the central part
of the Kwinte Bank (Figure 2.), which includes an elongated
depression (5 m deep, 700 m wide and 1 km long); this is the
morphological result of intensive dredging identified in 1999,
which subsequently lead to the decision of the Belgian Government, in 2003, to stop dredging for a period of at least 3
years, hoping to the regeneration of the bank.
The bank itself has an asymmetric morphology; its crest
lies along its western flank, which deepens to the WSW,
Figure 1. Geographical location of the Kwinte Bank, in relation to the
North Sea (inset) and the Belgian Continental Shelf.
with slopes of up to 5%. The crest itself lowers from the SW
to NE, with water depths on both sides being deeper than
10 m. The eastern flank of the bank slopes are more gently
(1.5-3%), towards the SE. Over this area, bedforms, such as
sand waves and megaripples, are present extensively; they
are of various wavelengths, heights, orientations and asymmetrical patterns. These bedforms consist mainly of wellsorted sands (200-400 μm), with a very small gravel fraction (LANCKNEUS, 1989). A detailed morpho-sedimentological
analysis of the study area is presented elsewhere (BELLEC et
al., this volume).
Some former studies undertaken into sediment transport
pathways over the region have been undertaken; however,
they were located over the northern part of this particular
bank and did not include the central depression (GAO et al.,
1994; LANCKNEUS, DE MOOR, and STOLK, 1994; and VANWESENBEECK and LANCKNEUS, 2000). Analysis of the bed morphology
indicates a general NE direction of sediment transport, coinciding with the direction of the flood currents (VANWESENBEECK
and LANCKNEUS, 2000). The grain-size trend analysis, applied
to the northern part of the Kwinte Bank, showed a similar
direction for the western flank of the bank, whilst its eastern
flank has a NW direction; this becomes SW, at water depths
of more than 20 m (GAO et al., 1994). Differences between
sediment transport directions given by the grain-size trend
analyses, with those indicated by bedform morphometry (e.g.
megaripples), may be attributed to their different spatial- and
time-scales of operation. The former are influenced often by
other local structural (geological) characteristics and, being
the result of extreme events, occurred over a much longer period of time (tens to hundreds of years).
Figure 2. Morphological characteristics and sampling positions
(for details, see text) of the Kwinte Bank.
Journal of Coastal Research, Special Issue No. 51, 2010
European Marine Sand and Gravel Resources
DATA COLLECTION AND METHODOLOGY
In September 2003 and February 2004, 120 samples (from
the same locations) were collected with the use of a van Veen
grab, during MAREBASSE / EUMARSAND campaigns (R/V
Zeeleeuw). The interval between successive stations was 300
m on the edges of the grid and 150 m over the central dredged
depression (Figure 2.).
The samples have been sub-sampled and analysed, following decarbonising with an HCl solution, in order to estimate
and remove the biogenic fraction (the shell content), as the
present investigation focuses upon the transport pathways of
the non-biogenic sediment component. Moreover, the biogenic
fraction of the sediment was removed for analytical reasons,
i.e. to improve the accuracy of the grain-size trend analysis.
The shell content incorporates usually a bimodal grain-size
distribution, resulting in inaccuracy in the grain-size determination using settling velocities; its abundance on the sea floor
is variable, depending upon localised benthic environmental
conditions.
In addition, shell fragments are somewhat different from
the quartz grains, in terms of their density and morphology; as
such, they differ in terms of their settling, transport and sorting characteristics. Besides, shell fragments are not usually
uniformely distributed over the seabed; they are more abundant in some areas, being rare in other; they follow not exclusively near-bed hydrodynamics, but also the local biologic
production (benthic and/or neritic). Hence, the use of the bulk
sediment would have introduced some additional differences
into the sediment texture, related to sediment transport.
Following decarbonising, sediment samples were analysed,
by means of a settling tower, to determine the settling velocities (Ws) of the individual particles; these, in turn, have been
converted into equivalent sieve diameters, according to the
SOULSBY (1997) equations. Sediment grain-size fractions were
identified according to the Wentworth classification (1922);
their statistical parameters needed for the trend analysis
method, i.e. mean grain-size, sorting, skewness, were calculated using statistical moment theory (RIVIERE, 1977).
For the determination of sediment transport pathways,
using the statistical parameters of the grain-size analyses,
the procedure described by GAO and COLLINS (1992) has
been adopted. This method is based upon the relationship
between spatial changes in grain-size trends and the residual transport directions. Thus, grain-size parameters are
compared between pairs of sampling sites, considering the
increase or decrease in three parameters: mean grain-size
(Mz), sorting (σI) and skewness (Sk). Consequently, 8 cases
are theoretically possible; of these, only 2 are representative
of physical reality in non-extreme marine conditions (GAO
and COLLINS, 1992; GAO and COLLINS, 1994a; and MCLAREN
and BOWLES, 1985). If transport takes place from Site 1 to
Site 2, 2 cases can be valid, either Case 1: σI2≤σI1, Mz1>Mz2,
and Sk2≤Sk1 (in a downstream direction, sediment becomes
finer, better sorted and more negatively skewed); or Case 2:
σI2≤ σI1, Mz2>Mzl, and Sk2≥Sk1 (sediment becomes coarser,
better sorted and more positively skewed). Notably, these
two cases do not represent extreme environments, in which,
for example, sediment is trapped or reworked intensively,
or transport agents are not selective. For this reason, a
three-step approach has been followed: the first step, as proposed by GAO and COLLINS (1992), consists of the verification
that the two aforementioned cases are indeed valid for a
study area (see below); the second step refers to the calculation of the three grain-size parameters (according to FOLK,
1974), by means of the equations issued from the statistical
89
moment theory (RIVIERE, 1977); and, finally, the third step
incorporates the application of the computerised analytical
procedure developed by GAO (1996), to the calculation of the
transport vectors.
The Kwinte Bank is under the influence of tidal currents
and oscillatory flows related to wave activity, which are selective transport agents; this means that the particle sorting,
in all cases, increases in the downstream direction. Furthermore no sediment accumulation has been observed over the
study area between 1992-1997 (DEGRENDELE et al., this volume), which is consistent with the relatively “homogeneous”
grain-size distribution pattern. Therefore, the two aforementioned cases are expected to be representative of the local
non-biogenic sediment transport, in the case of the Kwinte
Bank area. Realising step 3 (see above), initially, a critical
maximum distance (Dcr) has to be selected between two
neighbouring sampling sites, whose grain-size parameters
are compared. Thus, with the use of all sampling locations,
contour maps for the grain-size statistical parameters of the
area under investigation has been created; then, common
data points have been re-sampled every 300 m, in order to
produce a grid with even Dcr.
Subsequently, dimensionless “trend vectors” are drawn between every two sites (separated by Dcr), following the GAO
and COLLINS (1992) procedure; this is based, for a single analysis, upon the consideration of the two types of transport occurring at the same time, i.e. a combination of Case 1 and Case
2. Finally, the following calculations are undertaken for each
site: (1) the “resultant vector”, which is the sum of the trend
vectors; and (2) the “transport vector”, calculated with the filtering procedure developed by GAO and COLLINS (1992, 1994a).
This approach allows the resultant vectors from the neighbouring sites (e.g. within the Dcr), to be taken into account;
this in turn, leads to the calculation of a weighted-average.
Subsequently, these produce all the transport vectors of the
pattern of the residual transport, which enables recognition of
the main transport directions.
It should be noted that it is impossible to attribute any
quantitative significance to the length of these composite
transport vectors, without introducing a bias towards one of
the grain-size parameters (LE ROUX, 1994). Hence, with the
use of the GAO and COLLINS (1992) method only the sediment
transport pathways are determined and not the associated
transport rates.
Figure 3. Transport patterns: September 2003 (black arrows)
and February 2004 (grey arrows), shown in relation to the grain-size
distribution over the sampled area (see Figure 2.).
Journal of Coastal Research, Special Issue No. 51, 2010
90
Poulos and Ballay
RESULTS AND DISCUSSION
The results of the application of the GAO and COLLINS (1992)
procedure, applied to the results of both the sampling campaigns of September 2003 and February 2004, are presented
in Figure 3. The analyses of the two series of samples generate
generally similar results, which indicates the dominance of
relatively similar prevailing hydrodynamic conditions, either
for a short period of time prior to the (two) campaigns and/or
for the whole of the period between them.
Over the western part of the bank and, more specifically
along its crest area and the western flank of its central depression (formed by dredging), the transport vectors have a
NE orientation, indicating sediment transport towards the depression. Here, the bed material is composed of heterogeneous
medium to coarse shelly sand (shell content 40-55%) (BELLEC
et al., this volume). On the other hand, this vector direction
is in accordance with the main axis of the observed large bed
forms, i.e. the elongated subaqueous dunes. Further, it should
be noted that the direction of the vectors become progressively
NNE towards the northern part of the study area; finally, they
are directed northwestwards, at its northern limit. Here, the
crest of the bank is higher and the bank itself bends, with its
elongated axis being directed towards the North.
Within the lower (southern) and middle part of the dredged
area, the sediment transport vectors derived from both campaigns indicate a general NE direction of sediment transport;
at its northern part, the sediment transport pathways are directed towards the NNE. Once again, this change may be associated with the orientation of the existing mega-bedforms (e.g.
sand waves) and the morphology of the Kwinte Bank. Nevertheless, the artificially-made depression appears to act as a
sediment transport pathway, rather than being a depo-centre.
Here, the sediment are more homogeneous (Mz≈400 μm and
10-40% shell fraction; BELLEC et al., this volume). This interpretation is in accordance with the findings of DEGRENDELE et
al. (this volume), who state that over a period of 8 years (19921999), no significant morphological changes can be identified.
Furthermore, this pattern is in accordance with the observed
currents acting over the area (VAN DEN EYNDE et al., this volume), which permit the transport of these coarse and shelly
sediments. Overall, it appears that sediment is transported
from the crest, towards the eastern flank of the bank, despite
the presence of the dredged depression.
The gently-sloping eastern flank of the bank, characterised
by homogeneous fine to medium sand with a shell fraction
generally <20% (BELLEC et al., this volume), presents a transport pattern that could be distinguished into two sub-regions:
(a) a northern one, where the vectors are directed towards the
NNW; and, (b) a central/southern one, where vectors are more
or less directed southerly.
Some vectors located at the boundary of the study area may
show various orientations and directions; however, they have
not been incorporated into the analysis, having been attributed
to the ‘edge effect’. Transport vectors on the edge of the grid use
less neighbour points, for their calculation (GAO and COLLINS,
2001). The latter limitation would explain also some differences
in direction along the east boundary of the study area, between
the September 2003 and February 2004 results.
In terms of the prevailing tidal regime, the sediment transport pathways of the surficial non-biogenic (<2 mm) material
of the western side (crest and depression) of the bank appear
to be controlled by the flood phase of the tide, whilst its eastern flank by the ebb tide; this is in accordance to the residual
flows identified by GAREL (this volume). Moreover, the derived
transport pathways do not coincide with the mean flood/ebb
directions, as they are influenced also by the presence of bedforms and, more specifically, by the presence of asymmetrical
dunes (wavelengths >30 m) and megaripples (wavelength of
5-10 m) (LANCKNEUS et al., 1993). Furthermore, the influence of
wave activity, under storm conditions and, particularly for the
crest region of the bank, could not be excluded. For example,
in the case of similar sandbanks in the Bristol Channel (UK),
it has been established that the height of the banks is controlled by the storm conditions (BRITTON and BRITTON, 1980). The
latter observation is a matter for further investigation, relating to the combined effect of storms and tides.
Finally, if the findings of the present investigation are compared to those produced previously by GAO et al (1994), for the
northern end of the Kwinte Bank (where sediment pathways
are directed towards its crest, having an E-ESE direction
along its steep western flank and NW along its eastern more
gentle flank), on the assumption that the whole body of the
bank is subjected to the same hydrodynamic (tidal) regime,
then it may be concluded that the presence of the depression
(due to dredging) has modified significantly the near-bed hydraulic regime (GAREL, this volume). This regime now favours
the transport of sediment from the crest over the bank, towards its eastern flank. The pattern is in accordance with the
observations made by DEGRENDELE et al. (this volume), where
an overall lowering of the height of the bank (by ca. 0.5 m) has
been identified, between 1992 and 1999.
CONCLUSIONS
On the basis of grain-size trend analysis, the residual
transportation pattern reveals that, on the western steeper
slope and within the central depression of the bank, the principal transport pathway of the non-biogenic sandy material
is directed towards the northeast. Further, it can be assumed
that the relatively coarse (>500 μm) and less well-sorted (>1.2)
sediment, within these two sedimentary provinces, are associated with erosion (and/or transportation) during the flood
phase of the tide. However, wave action should not be excluded
from the analysis. Over the eastern gently sloping part of the
bank, characterised by medium sized (250-500 μm) sediments,
an overall southerly transport pathway is identified; this is
induced, most probably, by the ebb currents; although these
are weaker, they last longer and, as such, provides improved
sorting (<1.0) of the sediments. In addition, the presence of
the bedforms and the overall size of the bank appear to control
the sediment transport pathways. Finally, the presence of the
central depression appears to act as a ‘by-passing’ zone, rather
than as a depo-centre for sediments.
ACKNOWLEDGEMENTS
This study has been undertaken in accordance with the research objectives of the project EUMARSAND (“European Marine Sand and Gravel Resources: Evaluation and Environmental Impact of Extraction”, Contract No. HPRN-CT-2002-00222).
The authors thank Sophie Le Bot and Wendy Bonne for organising and performing the sampling campaigns, with the
assistance of Samuel Deleu, Els Verfaillie, Andrew Symonds
and Déborah Idier. The authors thank Michael Collins, Xaris
Plomaritis and Erwan Garel for their help during the grainsize analyses, at the School of Ocean and Earth Science in the
University of Southampton. Thanks are extended also to Vera
Van Lancker and Valérie Bellec, for the information provided
and their constructive comments.
Journal of Coastal Research, Special Issue No. 51, 2010
European Marine Sand and Gravel Resources
REFERENCES
BELLEC, V.; VAN LANCKER V.; DEGRENDELE K.; ROCHE R.; SCHOTTE P.,
and LE BOT S., this volume. Geo-environmental characterisation
of the Kwinte Bank. Journal of Coastal Research,
BRITTON R.C. and BRITTON S.R., 1980. Sedimentary bed forms and linear banks. In: COLLINS, M.B.; BANNER, F.T.; TYLER, P.A.; WAKEFIELD,
S.J., and JAMES, A.E. (eds.), Industrialised Embaymants and their
Environmental Problems. A case study for Swansea Bay. Pergamon
Press, 177-191
DEGRENDELE, K.; ROCHE, M.; SCHOTTE, P.; BELLEC, V., and VAN LANCKER,
V., this volume. Morphological evolution of the Kwinte Bank central depression after its closure. Journal of Coastal Research,
FOLK, P.L., 1974. Petrology of Sedimentary Rocks. Austin, Texas:
Hemphill Publishing Company, 183 p.
GAREL, E., this volume. Hydrodynamics and bedload transport, during a tidal cycle (derived from ADCP measurements), across the
Kwinte Bank. Journal of Coastal Research,
GAO, S. and COLLINS, M., 1991. A critique of the ‘‘McLaren Method’’ for
defining sediment transport paths. Journal of Sedimentary Petrology, 61, 143-146.
GAO, S. and COLLINS M., 1992. Net Sediment transport patterns inferred from grain-size trends, based upon definition of transport
vectors. Sedimentary Geology, 81(1/2), 47-60
GAO, S. and COLLINS, M., 1994a. Analysis of grain-size trends, for defining sediment transport pathways in marine environments. Journal
of Coastal Research, 10(1), 75-78.
GAO, S. and COLLINS, M., 1994b. Net sediment transport patterns inferred
from grain-size trends, based upon definition of ‘‘transport Vectors’’
reply. Sedimentary Geology, 90, 171-185.
GAO, S.; COLLINS M.; LANCKNEUS J.; DE MOOR G., and VAN LANCKER V.,
1994. Grain-size trends associated with net sediment transport
patterns: An example from the Belgian continental shelf. Marine
Geology, 121, 171-185
GAO, S., 1996. A fortran program for grain size trend analysis to define
net sediment transport pathways. Computers & Geosciences, 22(4),
449-452.
GAO, S. and COLLINS M., 2001. The use of grain-size trends in marine
sediment dynamics: a review. Chinese Journal of Oceanology and
Limnology, 19(3), 265-271.
HOWARTH, M.J. and PROCTOR, R., 1992. Ship ADCP measurementsand
tidal models of the North Sea. Continental Shelf Research, 12, 601623
HOUTHUYS, R.; TRENTESAUX, A., and DE WOLF, P., 1994. Storm influences
on a tidal sandbank’s surface (Middelkerke Bank, southern North
Sea). Marine Geology, 121, 23-41
LANCKNEUS, J., 1989. A comparative study of some characteristics of superficial sediments on the Flemish Banks. Int. Coll. Quat. Tert. Geology
Southern Bight, North Sea, May 1984. Ministry of Economic AffairsBelgian Geological Survey, 29-241.
91
LANCKNEUS, J.; DE MOOR, G.; DE SCHAEPMEESTER, G.; MEYUS, I., and
SPIERS, V., 1992. Residual sediment transport directions on a tidal
sandbank. In: Comparison of the “McLaren Model” with bedform
analysis. Bull. Belg. Ver. Aardr. Stud. (BEVAS) 2, pp. 425–446.
LANCKNEUS, J.; DE MOOR, G.; VAN LANCKER, V., and DE SCHAEPMEESTER,
G., 1993. The use of the McLaren model for the determination of residual transport directions on the Gootebank, southern North Sea:
Progress in Belgian Oceanographic Research. Institute of Marine
Research and Air Sea Interaction (IRMA), Vol. 1, pp. 75–94.
LANCKNEUS, J.; DE MOOR, G., and STOLK, A., 1994. Environmental setting, morphology and volumetric evolution of the Middelkerke
Bank (southern North Sea). Marine Geology, 121(1-2), 1-21.
LE ROUX, J.P., 1994. An alternative approach to the identification of
net sediment transport paths based on grain-size trends. Sedimentary Geology, 94, 97-107.
LIU, A.C.; MISSIAEN, T., and HENRIET, J.P., 1992. The morphology of the
top-Tertiary erosion surface in the Belgian sector of the North Sea.
Marine Geology, 105, 275-284.
MCLAREN, P.A., 1981. Interpretation of trends in grain-size measurements. Journal of Sedimentary Petrology, 51, 611-624.
MCLAREN, P.A. and BOWLES, D., 1985. The effects of sediment transport on grain-size distributions. Journal of Sedimentary Petrology,
55(4), 457-470.
MCLAREN, P., 2001. Sediment Trend Analysis (Sta (R)). Sea Technology, 42(3): 10-14.
MCLAREN, P. and BOWLES, D., 1991. A Critique of the Mclaren Method
for Defining Sediment Transport Paths - Reply. Journal of Sedimentary Petrology, 61(1), 147.
MCLAREN, P.; COLLINS, M.B.; GAO, S., and POWYS, R.I.L., 1993. Sediment
Dynamics of the Severn Estuary and Inner Bristol Channel. Journal
of the Geological Society, 150, 589-603.
MCLAREN, P.; CRETNEY, W.J., and POWYS, R.I., 1993. Sediment Pathways in a British-Columbia Fjord and Their Relationship with
Particle-Associated Contaminants. Journal of Coastal Research,
9(4), 1026-1043.
PETTIJOHN, F.G.; POTTER P.D., and SIEVER, R., 1972. Sand and Sandstone. New York: Springer, 618 p.
RIVIERE, A., 1977. Methodes Granulometriques; Techniques et Interpritations. In: MASSON, N. Paris (1977), 170p.
SOULSBY, R., 1997. Dynamics of marine sands: a manual for practical
applications. London: Thomas Telford, 249 p.
VAN DEN EYNDE, D.; GIARDINO, A.; PORTILLA, J.; FETTWEIS, M.: FRANCKEN,
F., and MONBALIU, J., this volume. Modelling the effects of sand
extraction on the sediment transport due to tides on the Kwinte
Bank. Journal of Coastal Research,
VANWESENBEECK, V. and LANCKNEUS, J., 2000. Sediment transport paths
on a tidal sand bank: a comparison between the modified McLaren
model and bedform analysis. Journal of Sedimentary Research,
70(3), 470-477.
Journal of Coastal Research, Special Issue No. 51, 2010